Notes
Name:_______________________________
2.5 Square Roots
Numbers such as 1, 4, 9, 16, and 25 are called _________________, because they are squares of __________.
A _________________ of a number is one of its two equal factors.
4 · 4 = 16, so 4 is the ___________________ of 16.
The symbol √
,called a _______________________ , is used to show a __________________ square root.
Find each square root. Think…what times itself gives you 81? (? · ? = 81)
√81
√196
√225
√49
√121
√16
Every positive number has TWO square roots: positive and negative.
The symbol for negative square root is:
−√25 shows the __________________ square root of 25.
Since (–5)² = 25, then −√25 = –5
±√25 shows both _____________________ and __________________ square root of 25.
±√25 = 5 and –5
−√81
±√49
√196
−√121
If n² = a, then n = ±√𝒂
c² = 9
b² = 169
m² = 289
c = ±√
b=
m=
c=
b=
m=
To place 25 chairs in a square arrangement, how many chairs should be in each row?
Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should
she plant in each row?
A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square
formation, how many will be in each row?
Area of a square is equal to the square of the length of a side.
A = s²
A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is
each side of the portrait?
The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each
square.
Area =
Area =
Area =
144 square
inches
49 square
feet
324 square meters
What is √−𝟐𝟓 ? Think…what times itself gives you –25? (? · ? = –25) ___________________________
Find each square root.
1. √16
2. −√9
3. √−36
4. −√196
5. ±√121
6. √−81
7. −√4
8. √289
Solve each equation
d² = 64
x² = 121
n² = 169
What if it is not a perfect square?
The square root of a number that is not a perfect square falls between two _______________ whole numbers.
Step 1 Determine whether a number is a perfect square.
1. Is the number 29 a perfect square? Is there a whole number which can be squared to equal 29? _____
Step 2 Find the two consecutive whole numbers between which the √𝟐𝟗 lies.
2. The number 25 is the closest perfect square _________ than 29. What is √25? _____
3. The number 36 is closest perfect square greater than 29. What is √36? _____
4. √29 lies between √25 and √36 . What are the two consecutive whole numbers between which √29
lies? _____________
Find the two consecutive whole numbers between which the square root of a given number lies.
Then circle the nearest integer.
√19 _______ _______
√57
_______ _______
√48 _______ _______
√99 _______ _______
√17
_______ _______
√2 _______ _______
***Under what condition is √𝑥 > √25 ?
Spiral Review
1) The radius of the Sun is 6.96 × 108 meters. Write this distance in standard form.
Write each expression using exponents
2) 6 · 6 · 6
5) What is absolute value of -18?
7) 8 – 2(5) =
1
3) 2 · 3 · 3 · 2 · 2 · 2
4) 1000
2
6) Find |− |
3
8) (–2)(3)(–5) =
Using the numbers 2, 3, and 4, write an example of the
9) Associative Property of Multiplication ________________ ; 10) Distributive Property ________________
HOMEWORK 2.5
1. Find each square root
√144
−√144
√−144
√25
√−9
−√100
√256
√−4
±√196
√225
−√169
√1
2. Solve each equation
d² = 400
x² = 289
n² = 121
3. Find the two consecutive whole numbers between which the square root of a given number lies.
Then circle the nearest integer.
√12 _______ _______
√96
_______ _______
√110 _______ _______
√3 _______ _______
√170
_______ _______
√55 _______ _______
4. Compare the following numbers using <, >, or = .
15 _____ √225
√625 _____ 2 × 101
502% ______ √16
11² _______ 1.21 × 103
5. Order the following numbers in ascending order.
1.5 × 10−2, 15%,
√15 ,
1
2
6. A marching band wants to form a square in the middle of the field. If there are 225 members in the band,
how many should be in each row?
7. If the area of a square is 529 square inches, what is the length of a side of the square?